the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 May 2026
Exchange rates, trade-offs and risks in mitigation options for aviation
Abstract. A recently proposed method to mathematically treat trade-offs and associated risks in aviation mitigation options (Prather et al., 2025) leaves, to this author's opinion, many issues open for discussion. The method is critically reviewed and the equations are derived and justified. Issues that remained vague in the recent paper are clarified. Unfortunately, close inspection proves this method to be inadequate for its purpose. An alternative formulation is proposed with transparent and understandable derivations. The unfounded assumptions basic to the original method are discussed and their effects on the final result are shown. It turns out that with the current data basis the proposed risk-analysis method for mitigation in aviation suffer from a certain degree of arbitrariness. Alternative approaches that exploit ensemble weather forecasts seem more promising.
- Preprint
(1120 KB) - Metadata XML
- BibTeX
- EndNote
Status: open (until 03 Jul 2026)
- RC1: 'Comment on jecats-2026-8', Anonymous Referee #1, 10 Jun 2026 reply
-
CC1: 'Comment on jecats-2026-8 with respect to the Prather, Gettelman & Penner paper', Michael Prather, 14 Jun 2026
reply
We are impressed by the effort Dr. Gierens put into his treatise dissecting the novel method we proposed to evaluate tradeoff mitigation options in a quantifiable risk framework (denoted PGP: M. Prather, A. Gettelman & J.E. Penner (2025) Trade-offs in aviation impacts on climate favour non-CO2 mitigation, Nature, 643, 988–995, 2025). we are also delighted that he took up the challenge of expanding the PGP approach and questioning where it might work, or where it might go wrong. It is good to have an open discussion here. Our paper closes with an open ended discussion of the problems and possible opportunities for our quantifiable risk application. We will go through the paper linearly, responding to Dr. Gierens’ interpretation of our paper and comparing that with what we had intended.
L32ff: We cannot understand how PGP is ad hoc, without ‘derivation’, and with unjustified uncertainties. We selected what was clearly available from the recent literature and admitted that it maybe was not good enough to make decisions yet. What we provided was a pathway and a decision risk curve that was clearly defined. Others (e.g., C. Voigt, 2025, Solving aviation’s climate-action conundrum, Nature 643 (8073), 921-923) have been able to follow the derivation and reproduce the base case.
L40ff: This discussion of tradeoff or exchange rate is semantics. GWPs are used for trading emissions, hence tradeoffs. I do not disagree with some of your approach but it is only words.
L51ff: Example 2 does not really work if we accept a “social cost” of carbon (which some do, but we might not) then the cosmogenic health problem can be readily costed and considered in tradoffs with CO2.
L84ff: “PGP assume … PDFs are log-normal”. This is an incorrect reading of the paper, In PGP, the PDFs of uncertainty can be in any form as long as it can be defined. They can even change sign if that is logical. We happened to select log-normal for the example shown. This is not a problem with the methodology.
The algebraic derivations beginning here are fine, but not applicable to the PGP general methodology. Gierens’ derivations focus entirely on carbon, which is core to the example in PGP, but the methodology can be applied to any climate tradeoff (or trading exchange rate).
L109ff: Yes, this is a good explanation of the PGP method, but veers off at L120.
L128: Yes, this is a very good point as to how these tradeoffs could be achieved in time, but that is so far outside the PGP paper. We did not go through the technology to define what CO2:contrail tradeoff was feasible.
L135: The complexity of what a tradeoff includes is indeed an interesting topic. For example, with the dual-annular combustors used for CO2:NOx tradeoffs, how are contrails impacted? This is an important study, but peripheral to the PGP work. Same with L154, the tradeoff will depend on specific situations with concrete numbers, but the PGP methodology can then provide a risk curve to describe the likelihood of a successful climate outcome.
L174: Sorry, NOx has two time scales (short O3 = ~1 month, and CH4 =~11 yr). But this whole discussion is irrelevant as long as we know the times scales (and their uncertainties) that are involved.
L213ff: This criticism is obscure and confusing. The community has generally accepted that a change in ERF can be transformed into a change in global mean temperature. That requires a great deal of faith in how we calculate ERF from a change in the atmosphere. There really is no absolute ERF value here, only a change in its value. It is a valid question of whether /how the change in ERF (for any constituent) from a fleet operating over several years can be scaled down to one airline or even one flight. Is this linear? Maybe for CO2, but I doubt it for NOx or contrails. This is a major scientific question for which we really do not yet have an answer. Parts of this are noted in PGP in the final discussion, but it is certainly outside its scope.
L231ff: Gierens’ math here is technically correct but introduces new variables (absolute ERF) that are unnecessary to the PGP tradeoff ratios. The problem with expanding ratios is that one can add terms that would otherwise cancel out, and these added terms induce an artificial uncertainty that should not be included. For example, the uncertainties in abs-ERF and ERF are highly correlated, and any uncertainty in abs-ERF will/should be propagated into the tradeoff ERF. The extra uncertainty in the example here, I believe is double counting.
This fundamental problem with uncertainty in ratios is why PGP specifically avoided any use of GWPs (e.g., GPW-CH4 = AGWP-CH4/AGWP-CO2) and stopped at the calculation of AGWP. If one wanted to do a mitigation tradeoff between CH4 and N2O, using the ratios of GWP-CH4:GWP-N2O with their individual uncertainties greatly exaggerates the uncertainty in the tradeoff because the uncertainty in AGWP-CO2 propagates into the GWP ratio. Instead we should start with AGWP-CH4 and AGWP-N2O. This problem gets even worse with contrails where a clear definition of causal emissions is not available.
L333ff: The Discussion wanders off into objections of using PGP method for a single flight, or the PGP choice of uncertainty PDFs, neither of which are core to the methodology. PGP is giving an example, and only speculates into specific cases where it might be applied.
The Conclusion wraps up with a long list of objections to the PGP methodology, many of which are based on a misreading of our conclusions and path forward, and others of which are based on the incorrect addition of uncertainties.
Gierens has included, here and throughout the paper, a number of important, very useful insights into how the PGP methodology could be used or misused. These ideas are valuable and need to be highlighted as they begin the scientific discussion and research on the way forward.
We support the comments of Anonymous Referee #1 (10 Jun 2026), which we just read before posting our comments, including the weakness of the PGP paper in adopting GWA as the climate metric. The methodology can and should be applied to alternative metrics to see if the risk curve between tradeoffs changes.
Michael Prather, UC Irvine
Joyce Penner, U. Michigan
14 June 2026
Citation: https://doi.org/10.5194/jecats-2026-8-CC1 -
RC2: 'Comment on jecats-2026-8', Anonymous Referee #2, 15 Jun 2026
reply
Aviation has much discussed effects on climate through its CO2 and non-CO2 emissions. The non-CO2 effects have inherently much larger uncertainties than the CO2 effects (in terms of effective radiative forcing, ERF). Mitigation measures tend to focus on technology, operations, and fuels, and often have so-called ‘tradeoffs’, where the non-CO2 effects may be reduced at the expense of an increase in CO2 effect. Prather et al address this. The present paper is a critique of the Prather et al approach, and as such is an important contribution. However, the present draft has some shortcomings which could be successfully addressed.
This is an important paper in the debate over operational mitigation approaches for aviation. Thus, some extra effort bringing some clarity, particularly to the style of presentation is worthwhile.
Abstract
The tone is quite critical of the original work and could be phased more equitably and factually. For example, “…leaves, to this author’s opinion, many issues open for discussion” could be “ leaves some issues open for discussion’ – indeed the original authors (Prather et al; hereafter PGP25) highlighted this. “Vague” could be “less clear”. The sentence “Unfortunately…” could be “The method proposed by PGP25 may have some shortcomings that are addressed with derivations presented here” (omit the next sentence). Remove “unfounded” “…suffer from a degree of arbitrariness” could be “..are highly dependent on the assumptions made, some of which are subjective or ‘user choices’” The last sentence needs to be put in context of what the present paper found in a more positive way (rather than the abstract reading as a list of criticisms of PGP25). At the moment, the last sentence is uninterpretable. Indeed, what this relates to is a rather passing comment at the end of the paper, which seems incomplete.
The abstract is currently letting a good paper down significantly and needs a complete re-think and re-write. Instead of focusing on the PGP25 problems and rather critical statements, the author should focus on some of the significant findings and interpretation that are present in the discussion.
Introduction
L10, the referencing is extensive but the outline non-specific. It would be helpful so say something like “a number of mitigation strategies have been proposed that require developments in technology, operations, and fuel type”.
L14 refers to tradeoffs, but is non-explicit. Many mitigation strategies do indeed imply compromises or tradeoffs, but the main problem lies in tradeoffs between short-lived climate forcers and CO2. This is the nub of the problem. There are other SLCF-SLCF tradeoffs but these are usually technological and of lesser consequence. It would be helpful to the reader to get to the core of the problem that is being addressed by PGP25 and the present paper. L15-21 identify the problem but not the critical issue (SLCF vs CO2) but omits to mention that the outcome of ‘positive for climate’ is potentially one that could even change sign over time.
L27 introduces the PGP25 metric but does not illuminate. Is it an AGWP per activity? In which case it is worthwhile to explain what the “Global Warming” is, since AGWP itself is a misnomer – it is simply an integrated RF over a user-chosen time horizon.
L32 “ad hoc, without derivation” is overly harsh. Please rephrase. Similarly, for the next two sentences, “not convincingly justified”, “vague” could be rephrased.
Critical review of the method of PGP
L41 I find the critique of PGP25 here entirely justified and the PGP25 sentence quoted rather muddles the history and usage of CO2 equivalence metrics. A tradeoff is an extension of the original intended usage of GWPs, as an exchange rate mechanism but has rather different implications. L:48 Example 1 is rather strange, going to the length of equating an individual source of CH4, and is not really illustrating successfully the equivalence/exchange rate mechanism originally intended. As originally conceived, GWP is a reporting convenience that recognizes different GHGs (and balances of a country, or sector) that by necessity requires an exchange rate mechanism, since the end effect of releasing (e.g.) 1 kg of CH4 is not the same as 1 kg of CO2. Also, by necessity, a time horizon (TH) needs to be specified, a compromise and subjective user choice that has been extensively debated in the literature since the concept of GWP was introduced in the late 1980s. Example 2 is correct, but seems unnecessarily off topic, and could be restated as the SLCF vs CO2 tradeoff, which has already been stated for NOx/fuel (and thus CO2), earlier. Example 3, is more to the point but identical in principle to Example 2.
L60, this is an oversimplification in that it omits the aspect of TH. TH has the potential to change the ‘outcome’, and should at least be acknowledged here.
It should also be noted that three are, as PGP25 noted, other CO2 equivalence metrics, notably the Global Temperature change Potential (GTP, Shine et al., 2005) and an alternative derivation of the GWP, the GWP* (Allen et al., 2015). These at least need to be mentioned as context somewhere (not necessarily in detail), earlier in the introduction of the concept and usage of CO2 equivalence emissions.
L67 “impossible”, at this point in the reading of the m/s, I would judge this to be incorrect (although the reader is directed forwards). Surely, the risk-analysis method will contain intrinsic uncertainties, and required some degree of user discretion and caution, but “impossible”?
2.2 Tradeoff risk
L78 – 80. This is a poor characterization of a particular GWP, in this case CH4. It is not a “best guess”, it is the best estimate of a ratio of an integrated RF from a pulse emission of CH4 divided by the same mass pulse emission of CO2. Both nominator and denominator have uncertainties, and the calculation will have assumptions of, e.g. background CO2 concentrations and TH selected. Dismissing it as a “best guess” is incorrect. The last part of L80 is correct in that the intrinsic uncertainties will make the decisions uncertain (in the sense of the efficacy of those decisions).
L98 “..if the GWA ratio is large…” I do not understand this. Surely, the success of the outcome is not simply dependent on the size of the ratio but the size of the uncertainties, particularly, in the nominator?
Finally, I note the PGP have themselves provided comments which are generally very helpful and I would recommend that the author consider these comments.
L156, for clarity and accuracy, please refer to CO2 equivalent emission metrics, not ‘climate metrics’ (see IPCC 1r6 glossary for what a ‘climate metric’ is generally agreed to be).
L213 I don’t understand this assertion. Yes, it is the ‘deltas’ that matter, but to some degree these will be dependent on the size of the absolutes, surely? For example, if the global ERF of contrail cirrus were 5 mW/m2, rather than 50 mW/m2, then that would affect the decision as to whether a mitigation measure was worthwhile. Hence, at this point, I disagree with the assertion and agree with that of PGP25 on “pressing need”.
L350 Bickel et al. (2025) are quite clear that an ERF for a single flight cannot be computed from a global computation, nor a local climate sensitivity parameter.
L364-367. Absolutely. This is the core finding. This has been potentially misrepresented or misunderstood by Voigt companion commentary to the PGP25 paper.
L404 Commendable – a widely ignored point. In general, there is a likelihood that an upwards vertical displacement for the purposes of avoidance will increase aviation induced ozone, and vice versa. Again, but for different reasons, the ERF of an individual flight is virtually impossible to compute robustly with chemistry-climate model. Similarly, the direct forcing of water vapour may operate similarly for altitudinal shifts.
L441 – L444. While agreeing completely, the author has not at any point dug into the practical difficulties that ERFs are only correctly computed with GCMs. Global integrations of plume calculations to derive a global RF, which is then corrected to an independent ERF/RF ratio are (as pointed out here and by Bickel et al. 2025) not valid. Avoidance calculations are carried out with plume calculations, at present, with mostly the single CoCIP model. The RF change of a flight is therefore not necessarily consistent with the global ERF (actually two different metrics), and an ERF of a single flight with a plume model without a coupled water vapour/energy budget, using a globalized adjustment is invalid.
L472 “hardly” could be replaces with “not” on the basis of the arguments presented.
L479 – L486 I understand what the author is alluding to, but I think that this is confusing issues. Presumably “weather forecasts” refers to accurate prediction of ice-supersaturation (for the formation of the individual persistent contrail in itself). PGP25’s work, seems to assume perfect prediction of contrail formation and persistence and deals with the tradeoffs of delta ERFs. I think that this point would be better dropped into the argument earlier, when summarizing the assumptions of the PGP25 work, rather than alluding to alternative methods later.
Final comments
I think in revising the paper, a better summary of what PGP25 are saying could be provided (see their comments on the present paper), rather than the sole focus on the mathematics of their risk calculations. They do indeed outline reservations over the usefulness and make some recommendations. Unfortunately, Nature-stable publications like “headlines” and the well-intentioned caveats of authors can get lost.
Style – the paper is extensively written in the first person, e.g. “to my feeling” L426, “To my view” L479, which I think is better phrased more passively voiced
Citation: https://doi.org/10.5194/jecats-2026-8-RC2
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 126 | 38 | 20 | 184 | 29 | 20 |
- HTML: 126
- PDF: 38
- XML: 20
- Total: 184
- BibTeX: 29
- EndNote: 20
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Summary
This paper engages with an important and genuinely underexplored problem: how to rigorously assess the risk that a proposed aviation climate mitigation measure will fail to deliver a net climate benefit, given the substantial uncertainties in aviation climate metrics. The motivation for critically examining Prather et al. (2025) (hereafter PGP) is reasonable, that paper does leave a number of methodological questions open. Unfortunately, the present manuscript does not succeed in either of the two goals it appears to pursue: it neither constitutes a sufficiently focused or complete critique of PGP, nor does it develop an alternative framework that is demonstrably more sound. For these reasons, and as elaborated below, I do not think the manuscript is suitable for publication in its current form. I do not believe these issues can be resolved through revision without what would amount to a substantially new paper, and I therefore recommend rejection, while encouraging the author to consider the paths forward suggested at the end of this review.
Major Comments
1. Unclear scope and contribution
The most fundamental problem with this manuscript is that it pursues two distinct goals simultaneously, a critique of PGP and the presentation of an alternative framework, without fully achieving either. This ambiguity undermines the paper throughout. A focused critical response to PGP, limited to identifying specific mathematical or conceptual errors, would more naturally take the form of a correspondence or comment submitted to Nature, where PGP was published. The present venue and format imply that the paper is making a positive contribution beyond critique, but the alternative framework presented here is not developed to a standard that would justify publication on its own terms. The author should decide which goal is primary and restructure accordingly. As it stands, the two goals pull against each other: the critique sections are sometimes too detailed for a paper primarily presenting new methodology, while the alternative framework is not developed rigorously enough to stand as an independent contribution.
2. The most important weakness of PGP is not addressed
The paper raises several legitimate concerns about PGP's mathematical presentation, but conspicuously omits what is arguably the most fundamental weakness of that paper and of the present one: the premise that a GWP-like metric provides a reliable basis for determining whether a mitigation action delivers a genuine climate benefit. GWP and GWA are time-horizon-dependent, globally and temporally averaged quantities that aggregate very different physical processes into a single number. The scientific literature contains extensive debate about whether such metrics are appropriate for decision-making, particularly when comparing long-lived forcing agents like CO₂ with short-lived ones like contrail-induced cirrus, see for example Shine et al. (2005, Climatic Change, 68, 281–302), who proposed alternatives to GWP precisely because of its limitations in comparing gases with very different atmospheric lifetimes, and Shine (2009, Climatic Change, 96, 467–472), who argued explicitly for a fundamental reappraisal of GWP as a policy metric. Fuglestvedt et al. (2010) provide a thorough overview of the metric landscape in the transport context, and Lee et al. (2021, 2023) discuss at length the difficulties of applying such metrics to aviation non-CO₂ effects specifically. By accepting the GWA framework as a valid foundation and confining the critique to mathematical implementation, this paper implicitly endorses a premise that deserves much more scrutiny. A paper positioning itself as a rigorous examination of PGP's methodology should engage seriously with this deeper issue.
3. The assumption that ERF changes are free of uncertainty is not justified
The central methodological claim of the alternative framework is that the right-hand side of the risk inequality, the ratio of ERF changes due to a mitigation measure, can be treated as a known, certain quantity because it is determined by a concrete operational or technical decision (lines 200–202). This assumption is very difficult to justify in practice and the paper does not seriously defend it. ERF changes are not directly controlled by operators; they are emergent outcomes of operational decisions mediated by complex atmospheric and microphysical processes. The change in contrail ERF resulting from a rerouting decision, for example, depends on ambient humidity, temperature, aircraft type, contrail microphysics, and radiative conditions — all of which carry substantial uncertainty. Further, ERF varies over the lifetime of a contrail, suggesting that even absent uncertainty, there wouldn’t be a one-to-one mapping between a re-routing decision and an ERF change, although this issue could be avoided by instead considering something like lifetime-integrated ERF. Treating ΔERFs as essentially known while locating all relevant uncertainty in the impulse response function parameters is not a physically motivated choice. It is an assumption made for mathematical convenience, and one that is arguably less realistic than PGP's treatment.
4. The contrail lifetime argument exposes an internal inconsistency
This issue is made concrete by examining what the left-hand side of equation (17) actually contains. The author claims that the relevant uncertainties reside in the parameters of the impulse response functions K_C(H), specifically the atmospheric lifetimes and decay timescales. For CO₂ this is reasonable; the multi-timescale decay of atmospheric CO₂ perturbations is a genuine and well-studied source of uncertainty. For contrail-induced cirrus, the impulse response function does include a lifetime parameter, and there is some genuine uncertainty in mean contrail lifetime. However, contrail lifetime is short enough (hours to at most a few days) that the integral K_CiC(H) is relatively insensitive to the precise value of that lifetime for any climatologically relevant time horizon H, the uncertainty in K_CiC(H) is small compared to the overall uncertainty in contrail climate forcing. This means that while the left-hand side of equation (17) carries some contrail-related uncertainty, it captures only a narrow slice of the total uncertainty associated with contrail forcing. The much larger sources of contrail climate uncertainty, including radiative properties, coverage, microphysics, and the relationship between operational decisions and actual contrail ERF, are not parameters of the impulse response function and therefore do not appear on the left-hand side at all. They must instead reside on the right-hand side, precisely where this paper claims everything is known. This is not a minor technical quibble; it is a structural problem that undermines the paper's central claim about where the relevant uncertainties lie.
5. The conclusion undermines the case for publication
The author states in the conclusions that "the method is not mature enough to base practical decisions on" and that "the stochastic model for the uncertainties is close to arbitrary." While this intellectual honesty is appreciated, it raises a question the paper does not adequately answer: what is the positive contribution being made? If the proposed framework is acknowledged to be immature and not actionable, and if its mathematical relationship to PGP is closer than claimed, then the manuscript needs to articulate much more clearly what a reader should take away from it. Scientific papers presenting methodological frameworks that are not yet fit for use need to make a compelling case for why the framework is nonetheless a meaningful step forward. That case is not made here.
Minor Comments
Recommendation and Paths Forward
For the reasons outlined above, I recommend rejection of the manuscript in its current form. The issues identified are not, in my view, resolvable through revision without producing what would effectively be a new paper. I want to be clear that this recommendation reflects the mismatch between the paper's scope and its execution, not a judgment that the underlying questions are unimportant. Indeed, they are important, and the aviation climate community would benefit from rigorous work on them.
I would suggest the author consider two potential paths forward. First, the specific mathematical criticisms of PGP, particularly the point about uncertain quantities appearing on both sides of the risk inequality, could be developed into a focused comment or correspondence submitted to Nature. This way the comment would reach the audience most directly engaged with PGP. Second, if the goal is to develop a genuinely alternative framework, the author should begin from a more critical examination of whether GWP-like metrics are an appropriate foundation at all, resolve the ERF uncertainty problem identified above, and ensure that the uncertainty structure of the proposed framework reflects the actual physical sources of uncertainty in aviation climate science rather than mathematical convenience. That would be a substantial and valuable contribution.